What is "Z Direction" in Force field?
The Z Direction setting is within the Falloff section of the Force Field settings and as such it defines how the force reduces in strength as you move along the z-axis. With it set to 'Both' it will decay in both directions, set to +Z in the positive direction only and with -Z in the negative direction only. 

Note also that the rate of falloff is determined by the 'Power' - with the Power set to 0 the force will always be distance^0 which will equate to '1' and so no actual falloff regardless of your Z Direction setting. Use a power of '1' for linear falloff, '2' for exponential fall off (such as with natural forces, gravity, etc.).